{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # 数据处理最重要的模块\n",
    "import pandas as pd # 数据处理最重要的模块\n",
    "import scipy.stats as stats # 统计模块\n",
    "import scipy\n",
    "# import pymysql  # 导入数据库模块\n",
    "\n",
    "from datetime import datetime # 时间模块\n",
    "import statsmodels.formula.api as smf  # OLS regression\n",
    "\n",
    "# import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt  # 画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "from matplotlib.font_manager import FontProperties # 作图中文\n",
    "from pylab import mpl\n",
    "mpl.rcParams['font.sans-serif'] = ['SimHei']\n",
    "plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "from pandas.tseries.offsets import MonthEnd\n",
    "\n",
    "#输出矢量图 渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell # jupyter运行输出的模块\n",
    "#显示每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 导入美国股票市场收益率数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1926-01-01</th>\n",
       "      <td>0.000561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-02-01</th>\n",
       "      <td>-0.033046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-03-01</th>\n",
       "      <td>-0.064002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-04-01</th>\n",
       "      <td>0.037029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-05-01</th>\n",
       "      <td>0.012095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-08-01</th>\n",
       "      <td>-0.020300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-01</th>\n",
       "      <td>-0.048003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-10-01</th>\n",
       "      <td>-0.029225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-11-01</th>\n",
       "      <td>0.093358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-01</th>\n",
       "      <td>0.053768</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1176 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   r\n",
       "month               \n",
       "1926-01-01  0.000561\n",
       "1926-02-01 -0.033046\n",
       "1926-03-01 -0.064002\n",
       "1926-04-01  0.037029\n",
       "1926-05-01  0.012095\n",
       "...              ...\n",
       "2023-08-01 -0.020300\n",
       "2023-09-01 -0.048003\n",
       "2023-10-01 -0.029225\n",
       "2023-11-01  0.093358\n",
       "2023-12-01  0.053768\n",
       "\n",
       "[1176 rows x 1 columns]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "US_market_ret = pd.read_csv(\"D:/ruo-ning/US stock market return.csv\")\n",
    "US_market_ret['month'] = pd.to_datetime(US_market_ret['month'],format='%Y-%m-%d')\n",
    "US_market_ret.set_index('month',inplace=True)\n",
    "US_market_ret.sort_index(inplace=True)\n",
    "US_market_ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>0.020353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>0.039647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.027064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>0.025048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.033909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-08-31</th>\n",
       "      <td>-0.020300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.048003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-10-31</th>\n",
       "      <td>-0.029225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-11-30</th>\n",
       "      <td>0.093358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>0.053768</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>348 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   r\n",
       "month               \n",
       "1995-01-31  0.020353\n",
       "1995-02-28  0.039647\n",
       "1995-03-31  0.027064\n",
       "1995-04-30  0.025048\n",
       "1995-05-31  0.033909\n",
       "...              ...\n",
       "2023-08-31 -0.020300\n",
       "2023-09-30 -0.048003\n",
       "2023-10-31 -0.029225\n",
       "2023-11-30  0.093358\n",
       "2023-12-31  0.053768\n",
       "\n",
       "[348 rows x 1 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "US_market_ret1 = US_market_ret['1995-01':'2024-09'].copy()\n",
    "US_market_ret1 = US_market_ret1.resample('ME')['r'].apply(lambda x: (1+x).prod()-1).to_frame()\n",
    "US_market_ret1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 描述性统计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    1176.000000\n",
      "mean        0.009298\n",
      "std         0.053350\n",
      "min        -0.291731\n",
      "25%        -0.018340\n",
      "50%         0.012866\n",
      "75%         0.039376\n",
      "max         0.394143\n",
      "Name: r, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# 进行描述性统计\n",
    "description = US_market_ret['r'].describe()\n",
    "print(description)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.127"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "7.549"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 统计检验\n",
    "US_market_ret['r'].skew().round(3)\n",
    "US_market_ret['r'].kurt().round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20%分位数: -0.024508\n",
      "正态性检验的 p 值: 5.234885212350629e-41\n",
      "数据可能不服从正态分布\n"
     ]
    }
   ],
   "source": [
    "# 20%分位数\n",
    "twenty_percentile = US_market_ret['r'].quantile(0.2)\n",
    "print(\"20%分位数:\", twenty_percentile)\n",
    "\n",
    "# 统计检验（例如，正态性检验）\n",
    "k2, p = stats.normaltest(US_market_ret['r'])\n",
    "print(\"正态性检验的 p 值:\", p)\n",
    "if p > 0.05:\n",
    "    print(\"数据可能服从正态分布\")\n",
    "else:\n",
    "    print(\"数据可能不服从正态分布\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>r</th>\n",
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       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-31</th>\n",
       "      <td>-0.039622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-29</th>\n",
       "      <td>0.031760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03-31</th>\n",
       "      <td>0.053499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-30</th>\n",
       "      <td>-0.059519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-31</th>\n",
       "      <td>-0.038863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-08-31</th>\n",
       "      <td>-0.020300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.048003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-10-31</th>\n",
       "      <td>-0.029225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-11-30</th>\n",
       "      <td>0.093358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>0.053768</td>\n",
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       "<p>288 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   r\n",
       "month               \n",
       "2000-01-31 -0.039622\n",
       "2000-02-29  0.031760\n",
       "2000-03-31  0.053499\n",
       "2000-04-30 -0.059519\n",
       "2000-05-31 -0.038863\n",
       "...              ...\n",
       "2023-08-31 -0.020300\n",
       "2023-09-30 -0.048003\n",
       "2023-10-31 -0.029225\n",
       "2023-11-30  0.093358\n",
       "2023-12-31  0.053768\n",
       "\n",
       "[288 rows x 1 columns]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 截取2000-2022年的数据\n",
    "US_market_ret_new = US_market_ret1['2000-01':'2024-09'].copy()\n",
    "US_market_ret_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
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   "source": [
    "fig, ax = plt.subplots(figsize=(15, 5)) # 图片比例\n",
    "ax.plot('r',  # 图片数据\n",
    "'.-',  # 线的类型\n",
    "color = 'g',  # 线的颜色 RGB\n",
    "label = 'US_Month_Return',  # 图片标签\n",
    "linewidth = 1,  # 线的粗细\n",
    "data =US_market_ret_new)  # 画图的数据\n",
    "ax.set_title(\"US Stock Market\") # 画图的标题\n",
    "ax.set_xlabel('month') # 画图的x轴名称\n",
    "ax.set_ylabel('Return') # 画图的y轴名称\n",
    "\n",
    "# 设置x轴的日期格式\n",
    "date_format = mdates.DateFormatter('%Y')\n",
    "ax.xaxis.set_major_formatter(date_format)\n",
    "\n",
    "# # 设置x轴的刻度间隔\n",
    "ax.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 旋转x轴标签以防止重叠\n",
    "plt.xticks(rotation=70)\n",
    "\n",
    "# 添加图例\n",
    "plt.legend(loc='upper left', frameon=False, fontsize=10)\n",
    "fig.savefig('US_Month_return.pdf', bbox_inches='tight')# 输出文件格式为pdf\n",
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   "metadata": {},
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制直方图\n",
    "plt.hist(US_market_ret_new['r'], bins=30)  # bins 表示直方图的条数\n",
    "\n",
    "# 添加标题和坐标轴标签\n",
    "plt.title(\"US Stock Market\") # 画图的标题\n",
    "plt.xlabel('Return') # 画图的x轴名称\n",
    "plt.ylabel('Frequency') # 画图的y轴名称\n",
    "\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rate</th>\n",
       "    </tr>\n",
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       "      <th>day</th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1950-01-31</th>\n",
       "      <td>1.07</td>\n",
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       "    <tr>\n",
       "      <th>1950-02-28</th>\n",
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       "      <td>5.50</td>\n",
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       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>5.00</td>\n",
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       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>5.00</td>\n",
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       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>4.75</td>\n",
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      ],
      "text/plain": [
       "            rate\n",
       "day             \n",
       "1950-01-31  1.07\n",
       "1950-02-28  1.07\n",
       "1950-03-31  1.07\n",
       "1950-04-30  1.07\n",
       "1950-05-31  1.07\n",
       "...          ...\n",
       "2024-07-31  5.50\n",
       "2024-08-31  5.50\n",
       "2024-09-30  5.00\n",
       "2024-10-31  5.00\n",
       "2024-11-30  4.75\n",
       "\n",
       "[899 rows x 1 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "funds_rate = pd.read_csv(\"D:/ruo-ning/Federal Funds2.csv\")\n",
    "funds_rate['day'] = pd.to_datetime(funds_rate['day'],format='%Y/%m/%d')\n",
    "funds_rate.set_index('day', inplace = True)\n",
    "funds_rate.sort_index(inplace = True)\n",
    "funds_rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 描述性统计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    899.000\n",
      "mean       4.424\n",
      "std        3.525\n",
      "min        0.250\n",
      "25%        1.350\n",
      "50%        4.000\n",
      "75%        6.000\n",
      "max       19.100\n",
      "Name: rate, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# 进行描述性统计\n",
    "description = funds_rate['rate'].describe().round(3)\n",
    "print(description)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.176"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.927"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 统计检验\n",
    "funds_rate['rate'].skew().round(3)\n",
    "funds_rate['rate'].kurt().round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20%分位数: 1.07\n",
      "正态性检验的 p 值: 6.992859535278492e-40\n",
      "数据可能不服从正态分布\n"
     ]
    }
   ],
   "source": [
    "# 20%分位数\n",
    "twenty_percentile = funds_rate['rate'].quantile(0.2)\n",
    "print(\"20%分位数:\", twenty_percentile)\n",
    "\n",
    "# 统计检验（例如，正态性检验）\n",
    "k2, p = stats.normaltest(funds_rate['rate'])\n",
    "print(\"正态性检验的 p 值:\", p)\n",
    "if p > 0.05:\n",
    "    print(\"数据可能服从正态分布\")\n",
    "else:\n",
    "    print(\"数据可能不服从正态分布\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 画图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
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       "            rate\n",
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       "2000-01-31  5.50\n",
       "2000-02-29  5.75\n",
       "2000-03-31  6.00\n",
       "2000-04-30  6.00\n",
       "2000-05-31  6.50\n",
       "...          ...\n",
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       "2024-06-30  5.50\n",
       "2024-07-31  5.50\n",
       "2024-08-31  5.50\n",
       "2024-09-30  5.00\n",
       "\n",
       "[297 rows x 1 columns]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 截取2000-2024年的数据\n",
    "funds_rate_new = funds_rate['2000-01-31':'2024-09-30'].copy()\n",
    "funds_rate_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
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       "   <g id=\"patch_4\">\n",
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       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 32.282812 298.7325 \n",
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       "   <g id=\"patch_6\">\n",
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       "   </g>\n",
       "   <g id=\"text_17\">\n",
       "    <!-- rate -->\n",
       "    <g transform=\"translate(385.99125 15.5325) scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#TimesNewRomanPSMT-72\"/>\n",
       "     <use xlink:href=\"#TimesNewRomanPSMT-61\" x=\"33.300781\"/>\n",
       "     <use xlink:href=\"#TimesNewRomanPSMT-74\" x=\"77.685547\"/>\n",
       "     <use xlink:href=\"#TimesNewRomanPSMT-65\" x=\"105.46875\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p77f13481d7\">\n",
       "   <rect x=\"32.282813\" y=\"21.5325\" width=\"725.4\" height=\"277.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 1300x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 5)) # 图片比例\n",
    "ax.plot(funds_rate_new['rate'],  # 图片数据\n",
    "'.-',  # 线的类型\n",
    "color = 'g',  # 线的颜色 RGB\n",
    "label = 'rate',  # 图片标签\n",
    "linewidth = 1.5,  # 线的粗细\n",
    "data = funds_rate_new['rate'])  # 画图的数据\n",
    "ax.set_title(\"rate\") # 画图的标题\n",
    "ax.set_xlabel('Time') # 画图的x轴名称\n",
    "ax.set_ylabel('rate') # 画图的y轴名称\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 直方图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([108.,  14.,   3.,  18.,  15.,   0.,   4.,  22.,  12.,   7.,  12.,\n",
       "          0.,   2.,   4.,   4.,   2.,   4.,   0.,   3.,   2.,   7.,   4.,\n",
       "          5.,   0.,  17.,  17.,   1.,   2.,   0.,   8.]),\n",
       " array([0.25      , 0.45833333, 0.66666667, 0.875     , 1.08333333,\n",
       "        1.29166667, 1.5       , 1.70833333, 1.91666667, 2.125     ,\n",
       "        2.33333333, 2.54166667, 2.75      , 2.95833333, 3.16666667,\n",
       "        3.375     , 3.58333333, 3.79166667, 4.        , 4.20833333,\n",
       "        4.41666667, 4.625     , 4.83333333, 5.04166667, 5.25      ,\n",
       "        5.45833333, 5.66666667, 5.875     , 6.08333333, 6.29166667,\n",
       "        6.5       ]),\n",
       " <BarContainer object of 30 artists>)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'rate')"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'rate')"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Frequency')"
      ]
     },
     "execution_count": 62,
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    "# 绘制直方图\n",
    "plt.hist(funds_rate_new['rate'], bins=30)  # bins 表示直方图的条数\n",
    "\n",
    "# 添加标题和坐标轴标签\n",
    "plt.title(\"rate\") # 画图的标题\n",
    "plt.xlabel('rate') # 画图的x轴名称\n",
    "plt.ylabel('Frequency') # 画图的y轴名称\n",
    "\n",
    "# 显示图形\n",
    "plt.show()"
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   "cell_type": "code",
   "execution_count": 63,
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   "outputs": [
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       "                   r  rate\n",
       "2000-01-31 -0.039622  5.50\n",
       "2000-02-29  0.031760  5.75\n",
       "2000-03-31  0.053499  6.00\n",
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     "execution_count": 63,
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   "source": [
    "reg_data = pd.merge(US_market_ret_new, funds_rate_new, left_index=True, right_index=True)\n",
    "reg_data =reg_data['2000':'2019']\n",
    "reg_data"
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   "execution_count": 64,
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       "     <!-- rate -->\n",
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       "    <g id=\"text_24\">\n",
       "     <!-- Return -->\n",
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       " <defs>\n",
       "  <clipPath id=\"pcacdc89b91\">\n",
       "   <rect x=\"32.282813\" y=\"21.5325\" width=\"725.4\" height=\"221.76\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 1300x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax1 = plt.subplots(figsize=(13,4))\n",
    "ax1.plot(reg_data['rate'],\n",
    "        color='red',\n",
    "        linestyle='-',\n",
    "        label='rate')\n",
    "ax1.set_ylabel('rate',color = 'red')\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(reg_data['r'].shift(1),\n",
    "        color='blue',\n",
    "        linestyle='-',\n",
    "        label='Return')\n",
    "\n",
    "ax2.set_ylabel('Return',color = 'blue')\n",
    "\n",
    "plt.title(\"US Stock Market Return and currency rate\")\n",
    "\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc=0)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 描述统计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    240.000\n",
       "mean       0.006\n",
       "std        0.044\n",
       "min       -0.185\n",
       "25%       -0.018\n",
       "50%        0.012\n",
       "75%        0.032\n",
       "max        0.116\n",
       "Name: r, dtype: float64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "count    240.000\n",
       "mean       1.847\n",
       "std        1.866\n",
       "min        0.250\n",
       "25%        0.250\n",
       "50%        1.250\n",
       "75%        2.500\n",
       "max        6.500\n",
       "Name: rate, dtype: float64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data['r'].describe().round(3)\n",
    "reg_data['rate'].describe().round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r      -0.677\n",
       "rate    1.096\n",
       "dtype: float64"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "r       1.298\n",
       "rate   -0.002\n",
       "dtype: float64"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data.skew().round(3)\n",
    "reg_data.kurt().round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 经济学基准模型\n",
    "$$\n",
    "r_{t} = \\alpha + \\beta rate_{t-1} + \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "- 原假设：$ \\beta = 0 $  美国股票的收益率与联邦基金利率不相关\n",
    "- 备择假设：$ \\beta \\neq 0 $\n",
    "    - H_1: $ \\beta >0$   正相关\n",
    "    - H_2: $ \\beta <0$   负相关\n",
    "- $R_t$ ：表示在t期时的收益率\n",
    "- 自变量X：rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      r   R-squared:                       0.011\n",
      "Model:                            OLS   Adj. R-squared:                  0.007\n",
      "Method:                 Least Squares   F-statistic:                     2.698\n",
      "Date:                Sat, 04 Jan 2025   Prob (F-statistic):              0.102\n",
      "Time:                        22:38:26   Log-Likelihood:                 410.71\n",
      "No. Observations:                 239   AIC:                            -817.4\n",
      "Df Residuals:                     237   BIC:                            -810.5\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "Intercept       0.0107      0.004      2.704      0.007       0.003       0.019\n",
      "lfunds_rate    -0.0025      0.002     -1.643      0.102      -0.005       0.000\n",
      "==============================================================================\n",
      "Omnibus:                       24.685   Durbin-Watson:                   1.843\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               33.797\n",
      "Skew:                          -0.678   Prob(JB):                     4.58e-08\n",
      "Kurtosis:                       4.247   Cond. No.                         3.98\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "reg_data['lfunds_rate'] = reg_data['rate'].shift(1)\n",
    "model_funds_rate=smf.ols('r ~ lfunds_rate',data = reg_data).fit()\n",
    "print(model_funds_rate.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      r   R-squared:                       0.011\n",
      "Model:                            OLS   Adj. R-squared:                  0.007\n",
      "Method:                 Least Squares   F-statistic:                     3.668\n",
      "Date:                Sat, 04 Jan 2025   Prob (F-statistic):             0.0567\n",
      "Time:                        22:38:56   Log-Likelihood:                 410.71\n",
      "No. Observations:                 239   AIC:                            -817.4\n",
      "Df Residuals:                     237   BIC:                            -810.5\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "===============================================================================\n",
      "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "Intercept       0.0107      0.004      2.717      0.007       0.003       0.018\n",
      "lfunds_rate    -0.0025      0.001     -1.915      0.055      -0.005    5.79e-05\n",
      "==============================================================================\n",
      "Omnibus:                       24.685   Durbin-Watson:                   1.843\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               33.797\n",
      "Skew:                          -0.678   Prob(JB):                     4.58e-08\n",
      "Kurtosis:                       4.247   Cond. No.                         3.98\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "model_funds_rate= smf.ols('r ~ lfunds_rate', data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC',\n",
    "    cov_kwds={'maxlags': 6}\n",
    ")\n",
    "print(model_funds_rate.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
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      ],
      "text/plain": [
       "<Figure size 1300x400 with 2 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_fit =reg_data.copy()\n",
    "data_fit['fitted_r'] = model_funds_rate.fittedvalues\n",
    "\n",
    "fig,ax1 = plt.subplots(figsize=(13,4))\n",
    "ax1.plot(data_fit['r'],\n",
    "        linewidth=1,\n",
    "        marker='o',\n",
    "        color='red',\n",
    "        linestyle='-',\n",
    "        label='r')\n",
    "ax1.plot(data_fit['fitted_r'],\n",
    "        linewidth=1,\n",
    "        marker='o',\n",
    "        color='blue',\n",
    "        linestyle='-',\n",
    "        label='fitted_r')\n",
    "ax1.set_ylabel('r',color = 'red')\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(reg_data['rate'].shift(1),\n",
    "        color='blue',\n",
    "        linestyle='-',\n",
    "        label=' rate')\n",
    "\n",
    "ax2.set_ylabel('rate',color = 'blue')\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "plt.xticks(rotation=90)\n",
    "plt.title(\"Return and fitted Return\")\n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "美国股票市场收益率与联邦基金利率之间的相关系数:-0.1041\n"
     ]
    }
   ],
   "source": [
    "r=reg_data['rate'].corr(reg_data['r']).round(4)\n",
    "print(\"美国股票市场收益率与联邦基金利率之间的相关系数:{}\".format(r))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 结论"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "联邦基金利率不能预测股票市场收益率的变化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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